On Babylon's rivers, there, we sat, also cried, in our remembering Zion.

and continues to describe the scene. Ibn Ezra cites some who hold that David authored the psalm with divine inspiration and was referring to the Babylonian exile, which was more than 400 years after his passing; the (later) M'tzudas David also holds of this view. (An alternative view is cited by ibn Ezra there, but for the purposes of this question assume David wrote it referring to later events.)

My question is how people (average Joes, not, say, David) of David's time and the 400-odd years thereafter understood the psalm. Did they know it referred to an impending Babylonian exile, just not know when it would be? Did they think it was metaphoric, referring to other things entirely? Did they think it was referring to a Babylonian exile, but one which (they thought) had been averted? Did they look at it and not have any idea what it meant? Or what?

2 Answers
2

I heard that Malbim discusses this issue. While he holds you can say that it was written at the time of the Churban, he also discusses how it could have been written by David. He raises two issues:

What would people have thought about such a mizmor before the churban?

What would happen to the mizmor if they did teshuvah and there was no churban?

He answers that David could have written it as a secret scroll that was passed down without being publicized. After the churban, the scroll was publicized and became part of tehillim. This avoids the "strangeness" of people reading such a mizmor during the time of e.g. Solomon.

Reading the Psalm itself, living at the time specified by the question, I would probably think that the Psalm's author was a captive in Babylon.
He sat there, in prison, waiting to get back. The psalm itself actually talks about "our captors (שובינו)":

"for there our captors asked us for songs, our tormentors demanded
songs of joy; they said, “Sing us one of the songs of Zion!”

I'm confused: he was a captive in babylon but not after the churban?
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Double AA♦Mar 28 '12 at 5:21

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They would probably guess that the author(s) has been to Babylon (trading?), where they were captured and wrote the poem: "for there our captors asked us for songs, our tormentors demanded songs of joy; they said, “Sing us one of the songs of Zion!”
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GuyMar 28 '12 at 7:16

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+1. I seem to recall something similar in Daas Soferim on this verse, although I'll have to look it up.
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AlexMar 28 '12 at 14:07

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Perhaps I'm a little late, but welcome to Judaism.SE Guy, and thank you for this answer! I hope to see you around the site!
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HodofHodApr 3 '12 at 2:12